Elsewhere, First Division side Salthill Devon will welcome St Patrick's Athletic to Drom Clubhouse, while Waterford United's reward for their First Round victory over Cobh Ramblers is a trip to Thomond Park to take on Limerick.
There are two all-Premier Division clashes as Bohemians face Bray Wanderers while Shamrock Rovers play host to Dundalk. All the games are set to take place on Monday and Tuesday, May 20th and 21st, with the eight quarter-finalists then matched up in an open draw.
EA Sports Cup Second Round Draw
Limerick v Waterford United
Wexford Youths v Cork City
Finn Harps v Derry City
Sligo Rovers v Mervue United
Bohemians v Bray Wanderers
Salthill Devon v St. Patrick’s Athletic
Drogheda United v Longford Town
Shamrock Rovers v Dundalk